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SageMath
E = EllipticCurve("bq1")
E.isogeny_class()
Elliptic curves in class 3150bq
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3150.bk1 | 3150bq1 | \([1, -1, 1, -725, -723]\) | \(461889917/263424\) | \(24004512000\) | \([2]\) | \(3072\) | \(0.68159\) | \(\Gamma_0(N)\)-optimal |
3150.bk2 | 3150bq2 | \([1, -1, 1, 2875, -7923]\) | \(28849701763/16941456\) | \(-1543790178000\) | \([2]\) | \(6144\) | \(1.0282\) |
Rank
sage: E.rank()
The elliptic curves in class 3150bq have rank \(1\).
Complex multiplication
The elliptic curves in class 3150bq do not have complex multiplication.Modular form 3150.2.a.bq
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.